The subject matter of this final thesis is the construction of a laboratory CNC milling machine with special emphasis on the Y axis of the same machine. The application of the milling machine is for educational purposes during laboratory exercises, so it is intended for machining of soft carbon steels. Through the introduction, a brief description of CNC machines will be given, with an emphasis on the Y-axis designs of such machines. The chip forming i.e. cutting process will be described also. After a brief description of the theoretical part of the final thesis, the calculation part begins by calculating the forces and velocities that occur on a given tool during the processing of the selected material. By the obtained values, the gantry and Y-axis drive will be dimensioned, all the necessary components and standard parts will be selected and displayed in the 3D model. The workpiece cooling system will also be calculated and dimensioned. In the conclusion of the final thesis, possible variations and similar solutions will be compared, as well as the observations during the construction process.